约束优化的两块校正非单调回代法(英文)  

A Two-piece Update Algorithm with Nonmonotonic Backtracking Technique for Constrained Optimization

作　　者：顾益明[1] 朱德通[1] 

机构地区：[1]上海师范大学数理信息学院,上海200234

出　　处：《上海师范大学学报（自然科学版）》2002年第4期8-15,共8页Journal of Shanghai Normal University(Natural Sciences)

基　　金：Science Grant of Shanghai Normal University(DQ17)

摘　　要：提出一种二块校正既约Hessian方法的非单调信赖域回代算法来解决约束优化问题。一般采用二块校正的双边既约Hesse阵方法代替完全Hesse阵方法处理大规模问题。为了获得算法的整体收敛性,引入非光滑的l_1罚函数作为势函数。在每次回代中不必使罚函数都单调递减,以使能克服高度非线性情况下的峡谷状态,同时采用二阶校正步计算能避免Maratos效应。只要每一步迭代至少运用两种校正规则之一,算法就能保持一步局部Q-超线性收敛速率。We propose a two-piece update of projected Hessian algorithm with trust region method for solving nonlinear equality constrained optimization problems. To deal with large problems, a two-piece update of two-side-reduced Hessian is used to replace the full Hessian matrix. By adopting the l1 penalty function as the merit function, a nonmonotonic backtracking trust region strategy is suggested which does not require the merit function to its value in every iteration. A correction step is avoided to overcome the Maratos effect. The proposed algorithm which switchs to nonmonotonic trust region strategy possesses global convergence while maintaining one step Q-superlinear local convergence rates if at least one of the update formula is updated in each iteration.

关 键 词：约束优化 非单调回代法 二块校正 超线性收敛 双边既约Hesse阵方法 罚函数 

分 类 号：O221.2[理学—运筹学与控制论]